Applied Complex Variables

The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of applications. This book explains clearly the fundamental ideas of time-domain scattering, including in-depth discussions of separation of variables and integral equations. The author covers both theoretical and computational aspects, and describes applications coming from acoustics (sound waves), elastodynamics (waves in solids), electromagnetics (Maxwell's equations) and hydrodynamics (water waves). The detailed bibliography of papers and books from the last 100 years cement the position of this work as an essential reference on the topic for applied mathematicians, physicists and engineers.

This book explains psychological, sociopolitical and organisational change in multidisciplinary settings. It shows how advanced techniques of contextual analysis can be applied to complex situations and offers a new cybernetic agency paradigm based on living systems theory. It models, diagnoses, and analyses complex, realworld situations to anticipate patterns of behaviour.

At present, much of the research on bilingual cognition focuses on late second language learners of a small number of languages. In this fascinating book, Evangelia Adamou widens the net by integrating advances in the field of bilingualism with the study of endangered languages. Drawing on recent studies from Europe and Latin America, she demonstrates that experimental psycholinguistic methods can be successfully applied outside the lab and, conversely, how data from these understudied populations provide new insights into the adaptive capacities of the bilingual mind. Adamou shows how bilinguals manage competing conceptualizations of time and space, how their grammars and language mixing patterns adapt to cognitive constraints such as the need for simplification, and how language processing concurrently adapts to their complex bilingual experience. Combining statistical analyses with detailed linguistic and ethnographic information, this essential book will appeal to scholars of bilin

The Systems Ecology Paradigm (SEP) incorporates humans as integral parts of ecosystems and emphasizes issues that have significant societal relevance such as grazing land, forestland, and agricultural ecosystem management, biodiversity and global change impacts. Accomplishing this societally relevant research requires cutting-edge basic and applied research. This book focuses on environmental and natural resource challenges confronting local to global societies for which the SEP methodology must be utilized for resolution. Key elements of SEP are a holistic perspective of ecological/social systems, systems thinking, and the ecosystem approach applied to real world, complex environmental and natural resource problems. The SEP and ecosystem approaches force scientific emphasis to be placed on collaborations with social scientists and behavioral, learning, and marketing professionals. The SEP has given environmental scientists, decision makers, citizen stakeholders, and land and water man

The Systems Ecology Paradigm (SEP) incorporates humans as integral parts of ecosystems and emphasizes issues that have significant societal relevance such as grazing land, forestland, and agricultural ecosystem management, biodiversity and global change impacts. Accomplishing this societally relevant research requires cutting-edge basic and applied research. This book focuses on environmental and natural resource challenges confronting local to global societies for which the SEP methodology must be utilized for resolution. Key elements of SEP are a holistic perspective of ecological/social systems, systems thinking, and the ecosystem approach applied to real world, complex environmental and natural resource problems. The SEP and ecosystem approaches force scientific emphasis to be placed on collaborations with social scientists and behavioral, learning, and marketing professionals. The SEP has given environmental scientists, decision makers, citizen stakeholders, and land and water man

Theories of social-ecological resilience have developed over the past decades and rapidly become an important framework for governance of complex non-linear environmental problems. This book explores the resilience theories and their compatibility with law, it identifies corresponding legal features. The legal features identified, including legal measures, mechanisms, principles and approaches, form a legal design for social-ecological resilience. A legal design that can be applied to different governance situations. It can be a tool both for designing new laws, as well as for assessing the effectiveness of current laws and legal systems. In many ways environmental law has adjusted and developed new approaches to meet complex environmental problems, but law is still challenged by the complexity that characterize environmental problems and the environmental change connected with the Anthropocene. This book provides a comprehensive review of the most fundamental components of the governa

The distinction between humans and the natural world is an artefact and more a matter of linguistic communication than a conceptual separation. This Element proposes ecosemiotics as an epistemological tool to better understand the relationship between human and natural processes. Ecosemiotics with its affinity to the humanities, is presented here as the best disciplinary approach for interpreting complex environmental conditions for a broad audience, across a multitude of temporal and spatial scales. It is proposed as an intellectual bridge between divergent sciences to incorporate within a unique framework different paradigms. The ecosemiotic paradigm helps to explain how organisms interact with their external environments using mechanisms common to all living beings that capture external information and matter for internal usage. This paradigm can be applied in all the circumstances where a living being (man, animal, plant, fungi, etc.) performs processes to stay alive.

本書初版於20世紀40年代，是經典的本科數學教材之一，對複變函數的教學影響深遠，被美國加州理工學院、加州大學伯克利分校、佐治亞理工學院，普度大學、達特茅斯學院、南加州大學等眾多名校採用。本書闡述了複變函數的理論及應用，還介紹了留數及保形映射理論在物理、流體及熱傳導等邊值問題中的應用。新版對原有內容進行了重新組織，增加了例題和圖、更加方便教學。

Voltaire's correspondence has been described as his 'greatest masterpiece' – but if it is, it is also his least studied. One of the most prodigious correspondences in Western literature, it poses significant interpretative challenges to the critic and reader alike. Considered individually, the letters present a series of complex, subtle, and playful literary performances; taken together, they constitute a formidable, and even forbidding, ensemble. How can modern readers even attempt to understand such an imposing work? This Element addresses this question through the use of digital reading methods and resources that enhance our understanding of this complex literary object and its relationship to Voltaire's more canonical literary output, and indeed to the Enlightenment world at large. Nicholas Cronk and Glenn Roe provide scholars and students with new pathways into this particular corpus, using tools and approaches that can then be applied to correspondences and life-writing texts in

A multitude of processes in hydrology and environmental engineering are either random or entail random components which are characterized by random variables. These variables are described by frequency distributions. This book provides an overview of different systems of frequency distributions, their properties, and applications to the fields of water resources and environmental engineering. A variety of systems are covered, including the Pearson system, Burr system, and systems commonly applied in economics, such as the D'Addario, Dagum, Stoppa, and Esteban systems. The latter chapters focus on the Singh system and the frequency distributions deduced from Bessel functions, maximum entropy theory, and the transformations of random variables. The final chapter introduces the genetic theory of frequency distributions. Using real-world data, this book provides a valuable reference for researchers, graduate students, and professionals interested in frequency analysis.

This new edition of a foundational text presents a contemporary review of cladistics, as applied to biological classification. It provides a comprehensive account of the past fifty years of discussion on the relationship between classification, phylogeny and evolution. It covers cladistics in the era of molecular data, detailing new advances and ideas that have emerged over the last twenty-five years. Written in an accessible style by internationally renowned authors in the field, readers are straightforwardly guided through fundamental principles and terminology. Simple worked examples and easy-to-understand diagrams also help readers navigate complex problems that have perplexed scientists for centuries. This practical guide is an essential addition for advanced undergraduates, postgraduates and researchers in taxonomy, systematics, comparative biology, evolutionary biology and molecular biology.

This new edition of a foundational text presents a contemporary review of cladistics, as applied to biological classification. It provides a comprehensive account of the past fifty years of discussion on the relationship between classification, phylogeny and evolution. It covers cladistics in the era of molecular data, detailing new advances and ideas that have emerged over the last twenty-five years. Written in an accessible style by internationally renowned authors in the field, readers are straightforwardly guided through fundamental principles and terminology. Simple worked examples and easy-to-understand diagrams also help readers navigate complex problems that have perplexed scientists for centuries. This practical guide is an essential addition for advanced undergraduates, postgraduates and researchers in taxonomy, systematics, comparative biology, evolutionary biology and molecular biology.

The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.

This text is geared toward students who have an undergraduate degree or extensive coursework in engineering or the physical sciences and who wish to develop their understanding of the essential topics of applied mathematics. The methods covered in the chapters form the core of analysis in engineering and the physical sciences. Readers will learn the solutions, techniques, and approaches that they will use as academic researchers or industrial R&D specialists. For example, they will be able to understand the fundamentals behind the various scientific software packages that are used to solve technical problems (such as the equations describing the solid mechanics of complex structures or the fluid mechanics of short-term weather prediction and long-term climate change), which is crucial to working with such codes successfully. Detailed and numerous worked problems help to ensure a clear and well-paced introduction to applied mathematics. Computational challenge problems at the end of eac

Now in its third edition, this textbook develops the economic way of thinking through problems that MBA students will find relevant to their career goals. Theory and mathematics are kept as simple as possible and illustrated with real-life scenarios. The textbook package includes online video tutorials on key concepts and complex arguments, and topics likely to be assessed in exams. The distinguished author team has developed this textbook over twenty years of teaching microeconomics to MBA students. Chapters are clearly structured to support learning: Part I of each chapter develops key economic principles, whilst Part II draws on those principles to discuss organizational and incentive issues in management and focuses on solving the 'principal-agent' problem to maximize the profitability of the firm - lessons that can be applied to problems MBA students will face in the future. Economics and management are treated equally; this unique textbook presents economics as part of the everyd

The essential guide for anyone wanting a quick introduction to the fundamental ideas underlying photonics. The author uses his forty years of experience in photonics research and teaching to provide intuitive explanations of key concepts, and demonstrates how these relate to the operation of photonic devices and systems. Readers will gain insight into the nature of light and the ways in which it interacts with materials and structures, and learn how these basic ideas are applied in areas such as optical systems, 3D imaging and astronomy. Carefully designed worked examples and end-of-chapter problems enable students to check their understanding, with full solutions available online. Mathematical treatments are kept as simple as possible, allowing readers to grasp even the most complex of concepts. Clear, concise and accessible, this is the perfect guide for undergraduate students taking a first course in photonics, and anyone in academia or industry wanting to review the fundamentals.

The essential guide for anyone wanting a quick introduction to the fundamental ideas underlying photonics. The author uses his forty years of experience in photonics research and teaching to provide intuitive explanations of key concepts, and demonstrates how these relate to the operation of photonic devices and systems. Readers will gain insight into the nature of light and the ways in which it interacts with materials and structures, and learn how these basic ideas are applied in areas such as optical systems, 3D imaging and astronomy. Carefully designed worked examples and end-of-chapter problems enable students to check their understanding, with full solutions available online. Mathematical treatments are kept as simple as possible, allowing readers to grasp even the most complex of concepts. Clear, concise and accessible, this is the perfect guide for undergraduate students taking a first course in photonics, and anyone in academia or industry wanting to review the fundamentals.

Analysing language data systematically and looking closely at how people formulate their thoughts can reveal astonishing insights about the human mind. Without presupposing specific subject knowledge, this book gently introduces its readers to theoretical insights as well as practical principles for systematic linguistic analysis from a cognitive perspective. Drawing on Thora Tenbrink's twenty years' experience in both linguistics and cognitive science, this book offers theoretical guidance and practical advice for doing cognitive discourse analysis. It covers areas of analysis as diverse as attention, perspective, granularity, certainty, inference, transformation, communication, and cognitive strategies, using inspiring examples from many different projects. Simple techniques and tools are used to allow readers new to the subject easy ways to apply the methods, without the need for complex technologies, whilst the cross-disciplinary approach can be applied to a diverse range of resear

Analysing language data systematically and looking closely at how people formulate their thoughts can reveal astonishing insights about the human mind. Without presupposing specific subject knowledge, this book gently introduces its readers to theoretical insights as well as practical principles for systematic linguistic analysis from a cognitive perspective. Drawing on Thora Tenbrink's twenty years' experience in both linguistics and cognitive science, this book offers theoretical guidance and practical advice for doing cognitive discourse analysis. It covers areas of analysis as diverse as attention, perspective, granularity, certainty, inference, transformation, communication, and cognitive strategies, using inspiring examples from many different projects. Simple techniques and tools are used to allow readers new to the subject easy ways to apply the methods, without the need for complex technologies, whilst the cross-disciplinary approach can be applied to a diverse range of resear

Nature-based solutions (NBS) are essential to ensure a sustainable society and healthy ecosystem over the coming decades. However, the systems to be managed are both broad and complex, requiring an integrated understanding of both bio-physical systems, such as soils and water, and economic and social systems, such as urban development and human behaviour. This edited book joins these domains of knowledge together from an applied perspective and considers how computer science can help. It takes a strategic look at the benefits and barriers to using modelling within environmental management and planning practice. It delves further by providing an in-depth comparative review of a wide range of models from a variety of scientific disciplines of interest with examples of their use for NBS. As such, this illustrated guide is designed to help students, researchers and practitioners navigate the huge range of modelling options available and develop the common understanding to work inter-discip

Anchored in simple and familiar physics problems, the author provides a focused introduction to mathematical methods in a narrative driven and structured manner. Ordinary and partial differential equation solving, linear algebra, vector calculus, complex variables and numerical methods are all introduced and bear relevance to a wide range of physical problems. Expanded and novel applications of these methods highlight their utility in less familiar areas, and advertise those areas that will become more important as students continue. This highlights both the utility of each method in progressing with problems of increasing complexity while also allowing students to see how a simplified problem becomes 're-complexified'. Advanced topics include nonlinear partial differential equations, and relativistic and quantum mechanical variants of problems like the harmonic oscillator. Physics, mathematics and engineering students will find 300 problems treated in a sophisticated manner. The insig

For anyone who wants to become a more effective writer, a more perceptive reader, and a more precise thinker, an understanding of English sentence structure is indispensable. This book shows you how to begin. Using clear and engaging examples from English, it introduces the basic concepts of syntactic structure to readers with no background in linguistics. Starting with simple, familiar phrases, and progressing to more complex sentences, it builds on what we already intuitively know, to provide a step-by-step account of why we understand these examples as we do. It then shows how that understanding can be applied to writing, helping us to avoid some of the common hallmarks of 'bad writing', such as ambiguity, redundancy, and vagueness. A unique and valuable resource, this book will enrich your understanding of English in ways that will make you a more effective user of the language. Publisher's note: The e-book edition of this title, like the print editions, contains color. For those e

For anyone who wants to become a more effective writer, a more perceptive reader, and a more precise thinker, an understanding of English sentence structure is indispensable. This book shows you how to begin. Using clear and engaging examples from English, it introduces the basic concepts of syntactic structure to readers with no background in linguistics. Starting with simple, familiar phrases, and progressing to more complex sentences, it builds on what we already intuitively know, to provide a step-by-step account of why we understand these examples as we do. It then shows how that understanding can be applied to writing, helping us to avoid some of the common hallmarks of 'bad writing', such as ambiguity, redundancy, and vagueness. A unique and valuable resource, this book will enrich your understanding of English in ways that will make you a more effective user of the language. Publisher's note: The e-book edition of this title, like the print editions, contains color. For those e

This innovative analysis investigates a complex issue of tremendous economic and political importance: what makes some countries vulnerable to banking crises, while others emerge unscathed? Banks on the Brink explains why some countries are more vulnerable to banking crises than others. Copelovitch and Singer highlight the effects of two variables in combination: foreign capital inflows and the relative prominence of securities markets in the domestic financial system. Foreign capital is the fuel for banks' potentially dangerous behavior, and banks are more likely to take on excessive risks when operating in a financial system with large securities markets. The book analyzes over thirty years of data and provides historical case studies of two key countries, Canada and Germany, each of which explores how political decisions in the 19th and early-20th centuries continue to affect financial stability today. The analyses in this book have crucial policy implications, identifying potential

Drawing on extensive corpus-based research, this book explores the nature and behavior of coordinate constructions in three case studies, covering order in copulative compounds, binomials (bare phrases), and more complex phrases. Historically, research on order in coordination has concentrated on so-called irreversible binomials, but Lohmann's research places significant focus on reversible ad hoc coordination and also presents a detailed comparison between irreversible and reversible binomials. This book uses empirical analyses to explore a wide range of factors, ranging from pragmatic to phonetic influences on the ordering process. It also offers readers a processing perspective on the results obtained, and puts forth a processing explanation for the characteristics of irreversible binomials. The book is ideal for researchers and advanced students working in English linguistics, syntax and psycholinguistics, and due to the multifactorial methodology applied it will be of particular i

Unique in its clarity, examples, and range, Physical Mathematics explains simply and succinctly the mathematics that graduate students and professional physicists need to succeed in their courses and research. The book illustrates the mathematics with numerous physical examples drawn from contemporary research. This second edition has new chapters on vector calculus, special relativity and artificial intelligence and many new sections and examples. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations, Bessel functions, and spherical harmonics, the book explains topics such as the singular value decomposition, Lie algebras and group theory, tensors and general relativity, the central limit theorem and Kolmogorov's theorems, Monte Carlo methods of experimental and theoretical physics, Feynman's path integrals, and the standard model of cosmology.

Geomicrobiology is the study of microbes and microbial processes and their role in driving environmental and geological processes at scales ranging from the nano, micron, to meter scale. This growing field has seen major advances in recent years, largely due to the development of new analytical tools and improvements to existing techniques, which allow us to better understand the complex interactions between microbes and their surroundings. In this comprehensive handbook, expert authors outline the state-of-the-art and emerging analytical techniques used in geomicrobiology. Readers are guided through each technique including background theory, sample preparation, standard methodology, data collection and analysis, best practices and common pitfalls, and examples of how and where the technique has been applied. The book provides a practical go-to reference for advanced students, researchers and professional scientists looking to employ techniques commonly used in geomicrobiology.

Quantum mechanics is traditionally associated with microscopic systems; however, quantum concepts have also been successfully applied to a diverse range of macroscopic systems both within and outside of physics. This book describes how complex systems from a variety of fields can be modelled using quantum mechanical principles; from biology and ecology, to sociology and decision-making. The mathematical basis of these models is covered in detail, furnishing a self-contained and consistent approach. This book provides unique insight into the dynamics of these macroscopic systems and opens new interdisciplinary research frontiers. It will be an essential resource for students and researchers in applied mathematics or theoretical physics who are interested in applying quantum mechanics to dynamical systems in the social, biological or ecological sciences.

How we vary our speech is fundamental in signalling who we are, where we're from and where we're going. How and when does such variation arise? Here, leading experts Jennifer Smith and Mercedes Durham address this question through a sociolinguistic analysis of the speech of preschool children in interaction with their primary caregivers. Bringing together two fields of linguistic research - variationist sociolinguistics and first language acquisition - the study focusses both qualitative and quantitative analysis of a range of variables to show when and how variation is acquired by young children, and the effect the caregiver's interaction has on this process. In doing so, they tackle a fundamental question in language research: when and how do children acquire the highly complex patterns of variation widely attested in adult speech?

Earthquakes are a huge global threat. In thirty-six countries, severe seismic risks threaten populations and their increasingly interdependent systems of transportation, communication, energy, and finance. In this important book, Louise Comfort provides an unprecedented examination of how twelve communities in nine countries responded to destructive earthquakes between 1999 and 2015. And many of the book’s lessons can also be applied to other large-scale risks.The Dynamics of Risk sets the global problem of seismic risk in the framework of complex adaptive systems to explore how the consequences of such events ripple across jurisdictions, communities, and organizations in complex societies, triggering unexpected alliances but also exposing social, economic, and legal gaps. The book assesses how the networks of organizations involved in response and recovery adapted and acted collectively after the twelve earthquakes it examines. It describes how advances in information technology enabl

Community is an evolving and complex concept that historians have applied to localities, counties, and the South as a whole in order to ground larger issues in the day-to-day lives of all seg

Community is an evolving and complex concept that historians have applied to localities, counties, and the South as a whole in order to ground larger issues in the day-to-day lives of all seg

Florence Thépot provides the first systematic account of the interaction between competition law and corporate governance. She challenges the 'black box' conception of the firm- or 'undertaking' - in competition law, as applied to increasingly complex corporate relations. The book opens the 'black box' of the firm to understand the internal drivers of collusive behaviour, and proposes a unified approach to cartel enforcement, based on the agency theory. It explores key issues including corporate compliance programmes, the attribution of liability in corporate groups, and structural links between competitors, and should be read by anyone interested in how the evolution of the corporate landscape impacts competition law.

Applied Theatre: Creative Ageing examines the complex social, political and cultural needs of a diverse group in our society and asks how contemporary applied theatre responds to those needs. It allow

This book examines the fragmentary and contradictory evidence for Orpheus as the author of rites and poems to redefine Orphism as a label applied polemically to extra-ordinary religious phenomena. Replacing older models of an Orphic religion, this richer and more complex model provides insight into the boundaries of normal and abnormal Greek religion. The study traces the construction of the category of 'Orphic' from its first appearances in the Classical period, through the centuries of philosophical and religious polemics, especially in the formation of early Christianity and again in the debates over the origins of Christianity in the nineteenth and twentieth centuries. A paradigm shift in the study of Greek religion, this study provides scholars of classics, early Christianity, ancient religion and philosophy with a new model for understanding the nature of ancient Orphism, including ideas of afterlife, cosmogony, sacred scriptures, rituals of purification and initiation, and exoti

Understand the benefits of robust statistics for signal processing with this authoritative yet accessible text. The first ever book on the subject, it provides a comprehensive overview of the field, moving from fundamental theory through to important new results and recent advances. Topics covered include advanced robust methods for complex-valued data, robust covariance estimation, penalized regression models, dependent data, robust bootstrap, and tensors. Robustness issues are illustrated throughout using real-world examples and key algorithms are included in a MATLAB Robust Signal Processing Toolbox accompanying the book online, allowing the methods discussed to be easily applied and adapted to multiple practical situations. This unique resource provides a powerful tool for researchers and practitioners working in the field of signal processing.

This volume provides an up-to-date, in-depth overview of the methods that have been applied to studying the complex metalloproteins at a molecular level. Chapters cover a wide range of approaches focu

Mental and Emotional Healing Through Yoga combines key research on the intersection of yoga and mental health with a client-centered, step-by-step framework that can be applied to a range of complex m

Mental and Emotional Healing Through Yoga combines key research on the intersection of yoga and mental health with a client-centered, step-by-step framework that can be applied to a range of complex m